A dynamic margin model takes shape

The general rule of thumb for margining an equity portfolio is to collect three times the 99% value-at-risk over a 10-day liquidation period. The problem with this type of static approach – which was laid bare when Archegos Capital Management collapsed in 2021 – is that it ignores the creditworthiness of the counterparty as well as the correlations and concentration levels of the underlying portfolio. 

Wujiang Lou, a director of quantitative trading at HSBC in New York, has spent several years working on a solution. His latest paper, published in Risk.net’s Cutting Edge section last week, proposes a model that dynamically adjusts haircuts and margin requirements for equity/long short portfolios in response to changes in a counterparty’s creditworthiness and the dynamics of the underlying portfolio. 

Portfolio returns are regressed against a market benchmark or index to derive the betas of individual stocks

The approach is strikingly intuitive. Portfolio returns are regressed against a market benchmark or index – such as the S&P 500 for US equities – to derive the betas of individual stocks. The betas represent the systematic component of the portfolio. For a truly market neutral portfolio, the sum of the beta would be zero. The idiosyncratic component of the portfolio is modelled as a jump process to account for sudden market gaps. The equity betas also give an indication of the correlation and diversification level of the portfolio, which can be reflected in the margin requirements. 

The paper also shows how to compute haircuts as a function of the loss distribution, while accounting for relevant variables such as concentration and directional biases. 

Jan Rosenzweig, a portfolio manager at Pine Tree, a hedge fund, says the approach has several advantages over existing methodologies. “This methodology applies a dynamic margining principle, by which one can track the change in the composition of the portfolio and adjust the margin accordingly,” he says. “I would expect margins to be lower in normal times, but to become steeper and steeper as a credit situation arises. In that sense, it would reward good risk management practices and penalise bad ones.

The model marks a significant step forward from a previous approach developed by Lou, which was able to dynamically calculate haircuts for long portfolios financed through repos or short portfolios funded by stock lending – but not both simultaneously. 

“This version allows netting and combining the long and short positions into one portfolio,” explains Lou. To do so, Lou had to change the haircut definition to a percentage of the gross rather than net market value, which in turn required a more robust jump diffusion estimation. 

The latest version of the model also captures one of the nuances of margining long/short portfolios. Opposing positions in highly correlated stocks are generally netted out, resulting in zero haircut. Lou’s model recognises that a market neutral strategy does not correspond to market neutral funding, due to the asymmetry between the repos and stock loans used to fund the long and short positions.  

“From the feedback so far, the model pretty much covers all major aspects of long/short mixed portfolio financing, and I expect at some point down the line it may be implemented by the market as a useful tool,” he says. 

The next step, he says, could be to extend the model to cover other asset classes, notably fixed income, though adapting the model for rates would add a further level of complexity. 

Pine Tree’s Rosenzweig suggests another direction could be to look at the market impact of unwinding large, concentrated positions, which was another factor in the losses sustained by banks that provided financing to Archegos.